Contextualised task 31 The World Land Record

Teaching Notes This task focuses on the World Land , which was set in Wales on four different occasions. Students study data and make conclusions. They choose appropriate calculations and graphs to support their analysis. Students may wish to carry out additional research, and the use of ICT would enhance the task.

Task A

Outline Students are introduced to the history of attempts. They study a data sheet and extract necessary information in order to draw conclusions about the size of increases in the world land speed record over time.

You will need: • Teachers’ script; • PowerPoint; • Question sheet; • Information sheet; • Spreadsheet; • Mark scheme.

Task B

Outline Students analyse a graph showing the growth of the land speed record. They consider how improvements should be made and produce their own time series graph.

You will need: • Questions sheet; • Information sheet; • Spreadsheet; • Mark scheme.

1

Tasks: Teachers’ script for PowerPoint presentation The text in the right-hand boxes provides a possible script to be read to students. However, it is probably preferable to use your own words and elaboration. When questions are asked, time for discussion in pairs/groups should be provided. Ensure that students are given to explain their reasoning in response to these questions. All students need to understand the concepts in order to make progress with the task.

Slide 1 Keep this slide on the screen until you are ready to start the presentation.

Land speed record

Slide 2 This is in South Wales. Pendine Sands is a 7-mile long beach with very flat and firm sand. It has been used as a venue for races for over 100 years. Since 1924 it has been used as a venue for speed record attempts. Slide 3 This is the first of several named ‘Blue Bird’. On 25 September 1924, drove it on Pendine Sands at an average speed of 146.16 miles per hour to set a new . The previous world land speed record, also set by a Briton, was 145.89 miles per hour.

What was the percentage increase in the world record speed? The actual difference was just 0.27 miles per hour, a percentage increase of 0.19% to two decimal places. Slide 4 On 21 July 1925 Malcolm Campbell increased this by another 4.71 miles per hour. What was the percentage increase in the land speed record this time? 3.22% This photo was taken on 21 July 2015 when Blue Bird had th a 90 anniversary drive on the beach. In the spring of 1926 a Welshman, John Godfrey Parry- Thomas increased the record by a further 12.68% in his car, ‘Babs’. What was the new land speed record at this time? 170 miles per hour Babs can be seen at the Pendine Museum of Speed.

2

Slide 5 The last time that a world land speed record was set at Pendine was in February 1927. Blue Bird II reached an average speed of 174.88 miles per hour.

Slide 6 The rules for world land speed records have developed since the very first record in 1898. For example, cars must carry out two runs in opposite directions. Why do you think this is? e.g. so that the effect of wind is minimised Rather than a maximum speed attained, it is their time over a fixed length that is recorded. Since 1964 the rules have also allowed jet- or -propelled vehicles. The UK has a history of interest in the world land speed record. Since the outbreak of World War I, there has only been a 20-year period when someone outside of Great Britain has held the record. It was last reclaimed for the UK by in 1983. He drove Thrust 2 at an average speed of 634.05 miles per hour.

Slide 7 And in 1997, Thrust SSC became the first car to break the speed of sound when (an RAF pilot with a first-class degree in Mathematics) reached an average speed of 763.04 miles per hour. This record still stands, although Richard Noble and Andy Green are aiming to set a new record with another vehicle. When Thrust SSC was being designed a 1:25 scale model was tested on a at Pendine Sands.

3

Task A: Question On 25 September 1924, Malcolm Campbell’s Blue Bird reached an average speed of 146.16 m.p.h. This broke the world land speed record with an actual increase of 0.27 m.p.h. and a percentage increase of 0.19%. On 21 July 1925 Malcolm Campbell increased this by 4.71 m.p.h. – a percentage increase of 3.22%. In 1927 John Godfrey Parry-Thomas, driving Babs, increased the record by 12.68%, which was an actual increase of 19.13 m.p.h.

Study the data provided on the information sheet. This shows every world land speed record that has been set since 1898. Find the lowest three actual increases in the record. Find also the lowest three percentage increases. Repeat for the highest three actual and percentage increases. Comment on your results.

You could use a spreadsheet to help with this task.

Task A: Information sheet

Speed Date Location Driver Vehicle mph km/h Achères, Yvelines, Gaston de 18 December 1898 Jeantaud Duc 57.65 92.78 Chasseloup-Laubat Achères, Yvelines, 17 January 1899 Camille Jenatzy La Jamais Contente 65.792 105.882 France 13 April 1902 Nice, France Léon Serpollet Easter Egg 75.06 120.80 Albis-St. Arnoult, William K. 5 August 1902 Mors 76.08 122.438 France Vanderbilt 12 January 1904 Lake St. Clair, USA Ford 999 Racer 91.37 147.05 26 January 1906 Ormond Beach, USA Fred Marriott Stanley Rocket 127.66 205.44 12 July 1924 France Ernest Eldridge FIAT Mephistopheles 145.89 234.98 25 September 1924 Pendine Sands, UK Malcolm Campbell Sunbeam 350HP 146.16 235.22 21 July 1925 Pendine Sands, UK Malcolm Campbell Sunbeam 350HP 150.87 242.8 28 April 1926 Pendine Sands, UK J.G. Parry-Thomas Babs 170 273.6 4 February1927 Pendine Sands, UK Malcolm Campbell Blue Bird 174.88 281.44 Mystery (Sunbeam 29 March 1927 Daytona Beach, USA 203.79 327.97 1000 hp) 19 February 1928 Daytona Beach, USA Malcolm Campbell Blue Bird 206.956 333.048 22 April 1928 Daytona Beach, USA Ray Keech Triplex Special 207.552 334.007 11 March 1929 Daytona Beach, USA Henry Segrave Golden Arrow 231.446 372.459 Verneuk Pan, South 5 February 1931 Malcolm Campbell Blue Bird 246.09 396.025 Africa 4

24 February 1932 Daytona Beach, USA Malcolm Campbell Blue Bird 253.97 408.73 22 February 1933 Daytona Beach, USA Malcolm Campbell Blue Bird 272.46 438.48 7 March 1935 Daytona Beach, USA Malcolm Campbell Blue Bird 276.816 445.472 Bonneville Salt Flats, 3 September 1935 Malcolm Campbell Blue Bird 301.129 484.598 USA Bonneville Salt Flats, 19 November 1937 Thunderbolt 311.42 501.16 USA Bonneville Salt Flats, 27 August 1938 George Eyston Thunderbolt 345.4 556.012 USA Bonneville Salt Flats, 15 September 1938 John Cobb Railton 350.2 563.566 USA Bonneville Salt Flats, 16 September 1938 George Eyston Thunderbolt 357.5 575.314 USA Bonneville Salt Flats, 23 August 1939 John Cobb Railton Special 369.74 595.04 USA Bonneville Salt Flats, 16 September 1947 John Cobb Railton Mobil Special 394.196 634.397 USA 17 July 1964 , Bluebird CN7 403.10 644.96 Bonneville Salt Flats, 2 October 1964 Tom Green 413.2 664.84 USA Bonneville Salt Flats, 5 October 1964 Art Arfons Green Monster 434.03 698.35 USA Bonneville Salt Flats, Spirit of America – 2 555.485 893.966 USA Sonic 1 Bonneville Salt Flats, Spirit of America – 15 November 1965 Craig Breedlove 600.601 966.37 USA Sonic 1 Bonneville Salt Flats, 23 October 1970 Blue Flame 622.407 1001.667 USA 4 October 1983 , USA Richard Noble Thrust 2 633.47 1019.47 25 September 1997 Black Rock Desert, USA Andy Green Thrust SSC 714.144 1149.303 15 October 1997 Black Rock Desert, USA Andy Green Thrust SSC 763.035 1227.986 Source: https://en.wikipedia.org/wiki/Land_speed_record

5

Task A: Mark scheme The information below is intended as a guide only.

Full credit Produces fully justified figures for the lowest three actual and percentage increases: Increase (m.p.h.) Details 0.27 Malcolm Campbell, Sunbeam 350HP (Blue Bird), 25.09.1924 0.596 Ray Keech, Triplex Special, 22.04.1928 1.02 William K. Vanderbilt, Mors, 05.08.1902

Percentage increase Details 0.19 Malcolm Campbell, Sunbeam 350HP (Blue Bird), 25.09.1924 0.29 Ray Keech, Triplex Special, 22.04.1928 1.36 William K. Vanderbilt, Mors, 05.08.1902 AND Fully justified figures for the highest three actual and percentage increases: Increase (m.p.h.) Details 121.455 Craig Breedlove, Spirit of America – Sonic 1, 02.11.1965 80.093 Andy Green, Thrust SSC, 25.09.1997 48.891 Andy Green, Thrust SSC, 15.10.1997

Percentage increase Details 39.72 Fred Marriott, Stanley Rocket, 26.01.1906 27.98 Craig Breedlove, Spirit of America – Sonic 1, 02.11.1965 20.10 Henry Ford, Ford 999 Racer, 12.01.1904 AND Makes incisive comments on the results; e.g. • When looking at the lowest increases, similar attempts appear near the end of both lists. Early in the history of breaking speed records, very small actual gains were made, and some of these were also very small percentage gains; • When looking at the highest increases, Craig Breedlove’s Spirit of America (Sonic 1) stands out in both lists (perhaps as this was about the time that rules were changed to allow jet- and rocket-propelled vehicles). Otherwise the largest percentage gains were made early on in the history of land speed records, despite the relatively small actual gains.

Partial credit Produces correct fully justified solutions for at least nine of the twelve values AND Makes incisive comments on the results OR Produces correct fully justified solutions for all twelve values

6

Limited credit Produces correct fully justified solutions for at least six values (including at least two correct percentage increases) AND Makes incisive comments on the results OR Clearly demonstrates how to find a percentage increase and round appropriately

No credit Any other response

7

Task B: Question Here is a scatter graph showing record number plotted against speed.

Speed (m.p.h.) 900

800

700

600

500

400

300

200

100

0 0 5 10 15 20 25 30 35 40

Record number

Describe what the graph tells you. Is it possible to make any predictions about future land speed record attempts? In what way is the graph misleading? Plot a time series graph showing date against speed. Comment on your graph.

Task 2: Mark scheme The information below is intended as a guide only.

Full credit Makes at least three incisive comments about the graph provided, e.g. • The rate of change of increase was fairly constant up until record number 29; • It would be easy to place a linear line of best fit between records 1 and 29; • The average rate of change between attempt 1 and 29 is about 13.5 m.p.h. per record; • There have been big jumps in speed throughout the last six records. AND Explains that it is not possible to make sensible predictions about any future records based on this graph

8

AND Identifies the fact that the record attempts were not equally spread over time AND Plots an accurate time series graph to show how the land speed record has changed over time. Note that there is scope for challenging levels of numerical reasoning when plotting this graph. As the accompanying spreadsheet demonstrates, the example has been constructed by calculating an estimate for the number of days elapsed since 18.12.1898. This estimate ignores leap years and uses 365/12 (=30.41666…) days in a month. Students may find using ICT more practical than plotting on paper. There is likely to be variation in the accuracy aimed for, and students operating at a higher level may not even be satisfied with the example here.

Speed (m.p.h.) 900

800

700

600

500

400

300

200

100

0 0 5000 10000 15000 20000 25000 30000 35000 40000

Number of days since first record set

AND Comments on their graph, e.g. • The ‘staircase’ shape might be influenced in part by the two world wars, which each correspond to a level section on the graph; • The period between the two world wars was the time when most attempts were made, and there was steady rise in the record throughout this period; • The development of technology has corresponded to the gap between attempts becoming much larger – there have only been two vehicles that have set a new record in the last 45 years. 9

Partial credit Creates an appropriately accurate time series graph AND Comments on the two graphs

Limited credit Creates an appropriately accurate time series graph OR Produces appropriately incisive comments in response to the questions, but the time series graph is incomplete or inaccurate.

No credit Any other response

10

Progression in reasoning Identify processes and connections • Identify, measure Read through the Identify all the As information is or obtain information given, information that is gathered, review its required and identify what needed to solve a usefulness, and information to might be useful problem, and how whether further complete the task information to gather this information information or next. might be obtained. different information Identify how this e.g. uses the dates to is required. information might be establish an e.g. makes and obtained. appropriate scale for justifies a decision e.g. identify that time plotting time on the about how to deal needs to be plotted horizontal axis of the with leap years against speed in order time series graph to produce a graph that provides more useful information Represent and communicate • Interpret graphs e.g. makes correct e.g. identifies what is e.g. analyses their own that describe comments about the misleading about the graph real-life graph provided graph provided situations, including those used in the media, recognising that some graphs may be misleading

Review • Interpret e.g. makes inferences e.g. discusses how the e.g. makes inferences mathematical using the graph provided graph should using their own graph information; provided not be used to make draw inferences inferences about from graphs, future events diagrams and data, including discussion on limitations of data

11

GCSE Content GCSE Mathematics – Numeracy and GCSE GCSE Mathematics only Mathematics Understanding number and place value • Rounding decimals to the nearest whole number or a given number of decimal places. Rounding numbers to a given number of significant figures. • Ordering and comparing whole numbers, decimals, fractions and percentages. Understanding number relationships and methods of calculation • Reading a calculator display correct to a specified number of decimal places or significant figures. • Finding a fraction or percentage of a quantity. • Expressing one number as a fraction or percentage of another. Solving numerical problems • Giving solutions in the context of a problem, selecting an appropriate degree of accuracy, interpreting the display on a calculator, and recognising limitations on the accuracy of data and measurements. • Rounding an answer to a reasonable degree of accuracy in the light of the context. Processing, representing and interpreting data • Constructing line graphs for the values of a variable at different points in time; understanding that intermediate values in a line graph may or may not have meaning. • Constructing and interpreting scatter diagrams for data on paired variables. Discussing results • Recognising that graphs may be misleading. Looking at data to find patterns and exceptions. • Drawing inferences and conclusions from summary measures and data representations, relating results back to the original problem. • Drawing of conclusions from scatter diagrams; using terms such as positive correlation, negative correlation, little or no correlation. Appreciating that correlation does not imply causality.

Key Foundation tier content is in standard text. Intermediate tier content that is in addition to foundation tier content is in underlined text. Higher tier content that is in addition to intermediate tier content is in bold text.

12